1,720,995 research outputs found
Complex extreme nonlinear waves: classical and quantum theory for new computing models
Full text linkThe historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines
Adiabatic evolution on a spatial-photonic Ising machine
Full text linkCombinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large
scale with conventional hardware.Novel optical platforms, knownas coherent or photonic Ising machines, are attracting
considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known
technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms,
electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical
settings has been only partially investigated.Here, we realize the adiabatic evolution of frustrated Ising models with 100
spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings
adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to
the Ising ground state and allows to find the problem solution with probability close to unity.Our results demonstrate a
photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and classical annealing
methods but enforced by optical vector-matrix multiplications and scalable photonic technology
Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics
Full text linkIt is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, such as the Hamiltonian. Resonances, i.e., states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism based on the so-called rigged Hilbert space (RHS). In the RHS, the states with complex energy are denoted as Gamow vectors (GVs), and they model decay processes. We study the GVs of the reversed harmonic oscillator, and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data that are not composed only by a summation of GVs, and we analyze different wave packets belonging to specific function spaces. Our work furnishes support for the idea that irreversible wave propagation can be investigated using rigged-Hilbert-space quantum mechanics and provides insight for the experimental investigation of irreversible dynamics
Imparare a sottotitolare. La didattica della traduzione tedesco-italiano con corti d'autore
No full textMachine learning inverse problem for topological photonics
Full text linkTopology opens many new horizons for photonics, from integrated optics to lasers. The complexity of large-scale devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a machine-learning approach applicable in general to numerous topological problems. As a toy model, we train a neural network with the Aubry–Andre–Harper band structure model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic design and by resorting to the widely available open-source TensorFlow library
Metriplectic Structure of a Radiation–Matter-Interaction Toy Model
No full textA dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a “Hamiltonian” and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, and a symmetric metric tensor, that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component is sufficient to describe the free electromagnetic radiation. The metric component encodes the radiation–matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption, and the radiation has disappeared. First, a description of the system is used, based on the real–imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase–amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics
Time Asymmetric Quantum Mechanics and Shock Waves: Exploring the Irreversibility in Nonlinear Optics
Full text linkThe description of irreversible phenomena is a still debated topic in quantum mechanics. Still nowadays, there is no clear procedure to distinguish the coupling with external baths from the intrinsic irreversibility in isolated systems. In 1928 Gamow introduced states with exponentially decaying observables not belonging to the conventional Hilbert space. These states are named Gamow vectors, and they belong to rigged Hilbert spaces. This review summarizes the contemporary approach using Gamow vectors and rigged Hilbert space formalism as foundations of a generalized “time asymmetric” quantum mechanics. We study the irreversible propagation of specific wave packets and show that the topic is surprisingly related to the problem of irreversibility of shock waves in classical nonlinear evolution. We specifically consider the applications in the field of nonlinear optics. We show that it is possible to emulate irreversible quantum mechanical process by the nonlinear evolution of a laser beam and we provide experimental tests by the generation of dispersive shock waves in highly nonlocal regimes. We demonstrate experimentally the quantization of decay rates predicted by the time-asymmetric quantum mechanics. This work furnishes support to the idea of intrinsically irreversible wave propagation, and to novel tests of the foundations of quantum mechanics
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